Fractals, Chaos, and Cancer: Do They Coincide?

Abstract

In the last years, several aspects of nonlinear dynamics have been explored in medical science (1-6) indicating the ubiquitous and pivotal role of dynamical processes. In general, cancer reflects a dynamical and multistage process (7,8). Complex and dynamical systems can be described mathematically by the chaos theory (9,10), which becomes visualized in fractal geometry (11). Therefore, one may ask whether a connection between chaos and cancer exists-and if so, does this knowledge lead to applications in diagnosis and/or therapy? Here, we attempt to interpret carcinogenesis in a chaodynamic manner at the cellular and the tissue level. We present fractal properties of tumor features well known in pathology. A fractal tumor appearance may indicate a basic power law that governs tumor growth. Considering the possible relationship between fractals, chaos, and cancer, we discuss potential applications of this new scientific approach in diagnosis and therapy of cancer.